A multivariate empirical Bayes statistic for replicated microarray time course data

In this paper we derive one- and two-sample multivariate empirical Bayes statistics (the MB-statistics) to rank genes in order of interest from longitudinal replicated developmental microarray time course experiments. We first use conjugate priors to develop our one-sample multivariate empirical Bayes framework for the null hypothesis that the expected temporal profile stays at 0. This leads to our one-sample MB-statistic and a one-sample T-2-statistic, a variant of the one-sample Hotelling T-2-statistic. Both the MB-statistic and T-2-statistic can be used to rank genes in the order of evidence of nonzero mean, incorporating the correlation structure across time points, moderation and replication. We also derive the corresponding MB-statistics and T-2-statistics for the one-sample problem where the null hypothesis states that the expected temporal profile is constant, and for the two-sample problem where the null hypothesis is that two expected temporal profiles are the same.